Analytical Model and Numerical Analysis of Composite Wrap ...

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Analytical Model and Numerical Analysis of Composite WrapSystem Applied to Steel Pipeline

Djouadi Djahida 1 , Ghomari Tewfik 2, Maciej Witek 3,* and Mechri Abdelghani 1

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Citation: Djahida, D.; Tewfik, G.;

Witek, M.; Abdelghani, M. Analytical

Model and Numerical Analysis of

Composite Wrap System Applied to

Steel Pipeline. Materials 2021, 14, 6393.

https://doi.org/10.3390/ma14216393

Academic Editor: Jae Hyuk Lim

Received: 6 June 2021

Accepted: 22 July 2021

Published: 25 October 2021

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1 Composite Structures and Innovative Materials Laboratory (LSCMI), University of Sciences and TechnologyUSTOMB, BP 1505, Oran 31000, Algeria; [email protected] (D.D.);[email protected] (M.A.)

2 Aeronautics and Propulsive Systems Laboratory (LASP), University of Sciences and Technology, USTOMB,BP 1505, Oran 31000, Algeria; [email protected]

3 Gas Engineering Group, Warsaw University of Technology, 20 Nowowiejska St., 00-653 Warsaw, Poland* Correspondence: [email protected]

Abstract: Composite overwraps are a cost-effective repair technology, appropriate for corrosiondefects, dents, and gouges for both onshore and offshore steel pipelines. The main benefit of polymer-based sleeves is safe installation without taking the pipeline out of service. This paper presents anew calculation procedure proposed in the form of an algorithm for the sizing of composite repairsof corroded pipelines when the sleeve is applied at zero internal pressure. The main objective of thepresented methodology is determination of the effective thickness of the composite repair withoutits overestimation or underestimation. The authors used a non-linear finite element method withconstitutive models allowing analysis of the steel, putty, and composite structures. The validation ofthe results of numerical computations compared to the experimental ones showed an appropriateagreement. The numerical calculations were applied to compare the analytical results in relation tothose obtained by the standards ASME PCC-2 or ISO/TS 24817. The comparison showed that theproposed solution confirmed its effectiveness in reducing the thickness of the sleeve significantly,thus, showing that the current industrial standards provide a considerably excessive composite wraparound the steel pipe corroded area, which leads to an unnecessary increase in the repair costs.

Keywords: composite overwrap repair; defected steel pipe wall; composite sleeve sizing; finite ele-ment analysis

1. Introduction

Pipelines are the safest and most economical way to transport various hydrocarbonproducts over long distances. However, as they are made of steel, they tend to degrade inthe corrosive environment. Furthermore, despite the availability of corrosion protectiontechnologies, underground structures are still susceptible to degradation with time ofoperation [1–3]. During inspections, scientists and engineers frequently deal with theproblem of tube wall metal loss, in particular, with its impact on the ability of the repairedthin-walled cylinder to withstand the design pressure [4]. For the unacceptable defects,in many service situations, the affected pipeline sections are removed and replaced withnew ones, or in some cases, full-encirclement steel sleeves are welded around the corrodedareas [5]. In both previously mentioned cases, such repairs entail significant costs due to themandatory shutdown of the pipeline, as well as the materials and installation expenditures.Before proposing a composite overwrap as a new competitor to steel sleeves for repairs,their use had not been recognized by high pressure network operators despite its extensiveapplication in many sectors, such as marine, automotive, and aerospace industries.

Since 2006, after the publication of international standards ASME PCC-2 [6] andISO/TS 24817 [7], the polymer-based laminate has been recognized as a new competitor tosteel sleeves for reinforcement of the tubes. As a result, the advantages of composite sleeves

Materials 2021, 14, 6393. https://doi.org/10.3390/ma14216393 https://www.mdpi.com/journal/materials

Materials 2021, 14, 6393 2 of 18

are widely accepted in pipeline renovation and have become a cost-effective approachdue to their effectiveness in improvement of long-term solutions and installation safety,as well as in reduction of a risk of an unplanned shutdown [8]. Considering the abovereasons, polymer-based materials for repairs of underground pressurized structures havebecome the subject of many publications. Regarding the development and qualificationof selection of composite materials for pipeline renovations, such studies as [9–16] wereanalyzed. The research focuses on improving the existing methodologies or developingnew ones, such as, but not limited to [17–24].

In regard to the design standards, the results of numerical and analytical research haveshown that ISO/TS 24817 and ASME PCC-2 lead to greater thickness of sleeves for smalland medium feature depths. In view of the foregoing, this paper presents a new analyticalapproach for providing the minimal thickness when the overwrap is applied at zero internalpressure. According to the authors’ best knowledge, it is the first time the effect of externalpressure has been taken into account. The external pressure can be considered to be animportant factor when repairing either trans-sea or buried onshore pipelines. In orderto include the effect of the putty material on the thickness to be calculated, the conceptof compound cylinders without shrinkage fit is used. The putty material is classified asan elastic isotropic material and the composite as elastic anisotropic material. The strain-hardening behavior is reached with the elasto-plastic stress–strain relationship of the steelpipe. To validate the effectiveness of the proposed design solution, a finite element analysis(FEA) approach was adopted in the present study.

2. Applied Methodologies

2.1. Standards ASME PCC-2 and ISO/TS 24817

With regard to ASME PCC-2 and ISO/TS 24817 standards [6,7], thickness tc of thereinforcement system can be calculated using the following general equation provided by:

εc =PdDext

2Ectc− S

ts

Ectc− PliveDext

2(Ectc + Ests)(1)

where Plive is the internal pressure at the time of the composite repair application, and Pdis the internal design pressure of the pipeline, Ec and Es are the elasticity moduli in thecircumferential direction of the laminate and steel, respectively, ts is the remaining thicknessof the pipe wall in the corroded zone, and tc is the minimum required thickness of thesleeve, Dext is the outside diameter of the steel tube, and εc is the composite allowable strain.

It should be noted that the difference between the two methods is included in the defi-nition of stress S: where S is defined as the specified minimum yield stress of steel, accordingto ASME PCC-2 code and as the admissible stress of the pipe wall according to ISO/TS24817. When the composite repair system is applied at zero internal pressure (Plive = 0),Equation (1) could be reduced as follows:

εc =PdDext

2Ectc− S

ts

Ectc(2)

However, ASME PCC-2 and ISO/TS 24817 standards neglect the putty materialcontribution and the strain-hardening effect.

2.2. Analytical Approach

Hypothetically, if the thickness of the steel tube, shown in Figure 1, is t0, and itsinternal radius is R0, and on its outer side, there is a rectangular corrosion defect of lengthc, sufficient width w, and maximum depth d, in order to repair this flaw using a compositeoverwrap system, the cavity of the metal loss needs to be filled with a high-compressive-strength epoxy putty. Then, the polymer-based laminate is applied circumferentiallyuntil the desired thickness tc is obtained. The compound cylinder is subjected to internalpressure Pi and to external pressure Pext.

Materials 2021, 14, 6393 3 of 18

Figure 1. A typical composite overwrap repair system.

Therefore, the purpose of the sizing is to calculate the minimum thickness tc of thepolymer-based sleeve to restore the load-bearing capacity of the damaged tube wall inorder to withstand the internal design pressure Pd. When the pressure Pi is applied,contact pressures are produced between three cylinders, shown in Figure 1. The contactpressures are as follows: Pc,1 at r = R1 (between the outer side of the steel and the innerside of the filling material) and the contact pressure Pc,2 at r = R2 (between the outer sideof the putty material and the inner side of the composite material). At r = R1, the steelpipe side and the putty material side are subject to stress in the circumferential, radial,and axial directions. The stress components can be found on each side of the cylinder usingLame’s relationships:

σsθ,1 =

R20Pi − R2

1Pc,1

R21 − R2

0+

(Pi − Pc,1)R20(

R21 − R2

0) (3)

σsr,1 =

R20Pi − R2

1Pc,1

R21 − R2

0−

(Pi − Pc,1)R20(

R21 − R2

0) (4)

σsa,1 =

R20Pi − R2

1Pc,1

R21 − R2

0(5)

and

σpθ,1 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1+

(Pc,1 − Pc,2)R22(

R22 − R2

1) (6)

σpr,1 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1− (Pc,1 − Pc,2)R2

2(R2

2 − R21) (7)

σpa,1 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1(8)

Moreover, at radius r = R2, the stress components can be found on the outer surfaceof the filling material and on the inner surface of the composite material:

σpθ,2 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1+

(Pc,1 − Pc,2)R21(

R22 − R2

1) (9)

σpr,2 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1−

(Pc,1 − Pc,2)R21(

R22 − R2

1) (10)

Materials 2021, 14, 6393 4 of 18

σpa,2 =

R21Pc,1 − R2

2Pc,2

R22 − R2

1(11)

and

σcθ,2 =

R22Pc,2 − R2

3Pext

R23 − R2

2+

(Pc,2 − Pext)R23(

R23 − R2

2) (12)

σcr,2 =

R22Pc,2 − R2

3Pext

R23 − R2

2−

(Pc,2 − Pext)R23(

R23 − R2

2) (13)

σca,2 =

R22Pc,2 − R2

3Pext

R23 − R2

2(14)

From Equations (4) and (7), the radial stress of both materials, namely, the steel of thepipe and the putty filler, at the contact interface r = R1 are defined as follows:

σsr,1 = −Pc,1 (15)

σpr,1 = −Pc,1 (16)

From Equations (10) and (13), the radial stress of the filler material and the compositesleeve material at the contact interface r = R2 are defined as follows:

σpr,2 = −Pc,2 (17)

σcr,2 = −Pc,2 (18)

In order to simplify the stress-pressure relationships, Equation (15) is substituted intoEquation (4) and rearranged as follows:

R20Pi − R2

1Pc,1

R21 − R2

0= −Pc,1(1 + α0) + α0Pi (19)

where:

α0 =R2

0(R2

1 − R20) (20)

Similarly, Equation (16) is substituted into Equation (7):

R21Pc,1 − R2

2Pc,2

R22 − R2

1= −Pc,1(1− α1)− α1Pc,2 (21)

where:

α1 =R2

2(R2

2 − R21) (22)

Additionally, Equation (17) is substituted into Equation (10):

R21Pc,1 − R2

2Pc,2

R22 − R2

1= −Pc,2(1 + α2) + α2Pc,1 (23)

where:

α2 =R2

1(R2

2 − R21) (24)

Finally, Equation (18) is substituted into Equation (13):

R22Pc,2 − R2

3Pext

R23 − R2

2= −Pc,2(1− α3)− α3Pext (25)

Materials 2021, 14, 6393 5 of 18

where:

α3 =R2

3(R2

3 − R22) (26)

Substituting Equations (19), (21), (23) and (25) into Equations (3)–(14), respectively,the following simplified expressions are obtained:

for the outer side of pipe steel:

σsθ,1 = −(1 + 2α0)Pc,1 + 2α0Pi (27)

σsr,1 = −Pc,1 (28)

σsa,1 = −(1 + α0)Pc,1 + α0Pi (29)

for the inner side of the filler material:

σpθ,1 = −(1− 2α1)Pc,1 − 2α1Pc,2 (30)

σpr,1 = −Pc,1 (31)

σpa,1 = −(1− α1)Pc,1 − α1Pc,2 (32)

for the outer side of the filler material:

σpθ,2 = −(1 + 2α2)Pc,2 + 2α2Pc,1 (33)

σpr,2 = −Pc,2 (34)

σpa,2 = −(1 + α2)Pc,2 + α2Pc,1 (35)

for the inner side of the composite material:

σcθ,2 = −(1− 2α3)Pc,2 − 2α3Pext (36)

σcr,2 = −Pc,2 (37)

σca,2 = −(1− α3)Pc,2 − α3Pext (38)

Assuming that the hoop stress at the outer side of the pipe reaches a given yieldingstress σs

θ,1 for a given internal pressure Pi, the contact pressure Pc,1 can be solved usingEquation (27).

Pc,1 = −σs

θ,1 − 2α0Pi

(1 + 2α0)(39)

In order to find the contact pressure Pc,2 at the interface r = R2, it is assumed thatthe radial displacement is the same for both the filler material and the composite materialup

r,2 = ucr,2. If it is known that the hoop strain can be related to radial displacement at any

radius r through as εθ = ur/r, the following relationship can be written:

εpθ,2 = εc

θ,2 (40)

As described previously, both the filler material and the composite material are sup-posed to be elastic. Thus, the hoop strains ε

pθ,2 and εc

θ,2 can be given as follows:

εpθ,2 =

1Ep

[σ

pθ,2 − vs

(σ

pa,2 + σ

pr,2

)](41)

εcθ,2 =

1Ec

θ

σcθ,2 −

(vc

rθ

Ecr

σcr,2 +

vcaθ

Eca

σca,2

)(42)

Materials 2021, 14, 6393 6 of 18

Substituting Equations (33)–(35) into Equation (41) gives contact pressure Pc,2 in thefollowing form:

Pc,2 =Pc,1(vp − 2

)α2 + Epε

pθ,2

α2(vp − 2

)+(2vp − 1

) (43)

It should be mentioned that if the hoop strain εcθ,2 equals the allowable strain εc of the

composite material, Equation (40) requires that εpθ,2 = εc. Thus, the contact pressure Pc,2

can be solved using Equation (43).Regarding the thickness of the repair tc, radius R3 needs to be determined first. Hence,

substituting Equations (36)–(38) into Equation (42) and rearranging the formula gives:

εcθ,2 = −Pc,2

[1

Ecθ

−(

vcaθ

Eca+

vcrθ

Ecr

)]+ α3(Pc,2 − Pext)

[2

Ecθ

−vc

aθ

Eca

](44)

Solving Equation (44) for geometric ratio α3 gives:

α3 =εc

θ,2 + Pc,2

[1

Ecθ−(

vcaθ

Eca+

vcrθ

Ecr

)](Pc,2 − Pext)

[2

Ecθ− vc

aθEc

a

] (45)

External radius of the composite sleeve R3 as a function of the geometric ratio α3 andthe external radius of the pipe R2 is obtained using Equation (26):

R3 = R2

√α3(α3 − 1)(α3 − 1)

(46)

Assuming that R3 = R2 + tc, Equation (46) can be rearranged to provide thickness tcof the composite polymer-based sleeve as:

tc = R2

[√α3(α3 − 1)(α3 − 1)

− 1

](47)

For the case in which terms(vc

aθ/Eca)

and(vc

rθ/Ecr)

can be neglected, compared tosignificance of the term

(1/Ec

θ

), Equation (45) can be simplified to:

α3 =Ec

θεcθ,2 + Pc,2

2 (Pc,2 − Pext)(48)

From Equation (48), it can be seen that the geometric ratio α3 becomes mostly depen-dent on mechanical properties of the laminate material in the circumferential direction.

Procedure to Find the Thickness tc Based on the Developed Approach

In this section, a novel algorithm for designing the repair thickness tc of a corrodedpipe using the composite material is presented. This solution is based on the formulasdeveloped in the previous section. The steps of the proposed new approach are describedin the flowchart in Figure 2.

If the pressure is substituted as Pi = Pd, the stress σsθ,1 = K

(εs

θ,1

)n(n is the strain-

hardening exponent) and the strain εcθ,2 = εc are reached. The applied solution can be used

to design a composite sleeve for recovering the initial design pressure Pd of the pipeline.This pressure is also referred to as the maximum allowable working pressure (MAWP).Pd is considered to be the relief pressure of the pipeline safety valves and is generally higherthan the maximum operating pressure (MOP). According to Code B31.8 [25], Pd is given as:

Pd = FET2t0

DextSMYS (49)

Materials 2021, 14, 6393 7 of 18

where F is a design safety factor, E is a longitudinal welding joint factor and T is a tempera-ture derating factor. In this paper, a value of 0.72 has been adopted for FET.

Figure 2. A flowchart for determining the thickness of a composite overwrap repair system.

If the pressure is substituted as the burst pressure Pi = Pb, the plastic stress

σsθ,1 = K

(εs

θ,1

)nand the strain εc

θ,2 = εc are reached. The proposed approach provides thecomposite sleeve thickness for reconstructing the initial load-carrying capacity of the tubeas burst pressure P0 of an intact pipe. A decision to repair a corroded cylinder generallydepends on its remaining load-carrying capacity, which should sufficiently withstand thedesign pressure. The remaining load-carrying capacity is carried out using ASME B31.Gcode [26]. Therefore, the burst pressure of a tube containing a metal loss is given as:

Pf =2t0

Dext(SMYS + 69 MPa)

1− 0.85 dt0

1− 0.85 dt0

1M

(50)

where z = c2/(Dextt0) is the normalized metal loss length, and M is the Folias factor:

M =

{ √1 + 0.6275z− 0.003375z2, z ≤ 0

0.032z + 3.3, z > 0(51)

A corrosion defect is considered to be acceptable when the calculated burst pres-sure is equal to or greater than the maximum value of the pressure set for the pipe(MAOP = 0.9 Pd) multiplied by a safety factor, usually not less than 1.25:

Pf /MAOP ≥ 1.25 (52)

Materials 2021, 14, 6393 8 of 18

2.3. Finite Element Analysis

While the steel tube and composite overwrap system are presumptive axisymmetricgeometrical structures, the numerical model can be directly simplified into a 2D model.The key to this assumption is that the effect of the corrosion width is marginal and doesnot compromise the model accuracy [27,28]. As it is shown in Figure 3, the pipe and therepair sleeve are assumed to be axially symmetric around the central axis y. For this reason,an axisymmetric analysis was performed using two-dimensional 8-node quadrilateral ele-ments (SOLID Plane 183) with the axisymmetric option activated. In addition, the pressurevessel is symmetric in respect to plane y = 0 running through the center of the cylindricalshell. Therefore, only a section of a quarter of the structure needs to be modeled.

Figure 3. Repaired pipe with pressure load and boundary conditions.

The internal pressure Pi is applied gradually, and when it reaches a value ofPi ≥ 0.9 Precovered, the internal pressure increment ∆Pi is insignificant and the numeri-cal pressurization becomes slow. The calculation process stops when one of the two failurecriteria is satisfied. These two criteria are the rupture criterion of the composite and theburst criterion of the pipe steel. The pressure obtained at the end of the calculation processis considered the maximum burst pressure.

Figure 4 illustrates a mapped mesh of a steel tube, metal loss with the putty filler,and the composite overwrap. The irregular geometry of the model was divided into fullybonded sub-areas in order to control element sizing effectively. Then, mapped mesh withregular PLAN 183 quad elements was applied. A total of 4040 quadrilateral elements and12,771 nodes were used.

Figure 4. A finite elements mesh model with magnification of the repaired zone.

3. Limit Load and Experimental Validation

To validate the numerical model as a viable method for the analysis of the pipelinerepair system, experimental results found in the literature [18,23] were used due to theavailability of all necessary data. Thus, one axisymmetric defect with 50% pipe wallthickness loss [18] and then one rectangular tube wall loss with 60% thinning [23] weremachined into pipes. The first specimen was repaired using carbon–epoxy composites,and the second was repaired applying a fiber-glass epoxy material. Tables 1 and 2 provide,

Materials 2021, 14, 6393 9 of 18

respectively, the necessary engineering data for the used steel tube and the mechanicalcharacteristics of the applied composites.

Table 1. Pipe material properties.

Reference [18] [23]Steel grade A106 Gr B GOST 8731-74

External diameter Dext (mm) 152.3 220Pipe wall thickness t (mm) 7.11 6.0

Yield stress σy (MPa) 300 (0.2% offset) 305 (0.2% offset)SMYS (MPa) 241.3 241.3

Poisson’s ratio vs 0.30 0.30Hollomon true σ− ε model 823.33ε0.1813 697ε0.136

Table 2. Laminate and filler material mechanical properties.

Reference [18] [23]Polymer-based laminate Carbon fiber/epoxy Glass fiber/epoxy

Modulus in the hoop direction Eθ (MPa) 49,000 48,470Modulus in the axial direction Ea (MPa) 23,400 6770Modulus in the radial direction Er(MPa) 5500 6770

Poisson’s ratio vra 0.45 0.4Poisson’s ratio vaθ 0.07 0.099Poisson’s ratio vrθ 0.45 0.099

Shear modulus Gra (MPa) 690 1670Shear modulus Gaθ (MPa) 2960 3200Shear modulus Grθ (MPa) 690 3200

Failure stress in hoop direction (MPa) 576 678Composite thickness tc (mm) 3.1 6

Filler MaterialYoung’s Modulus Ep (MPa) 1740 3300

Poisson’s ratio vp 0.45 0.37

ANSYS APDL software was used to numerically simulate the burst tests of two defectsof 50% and 60% tube wall thickness thinning. The engineering data presented in Tables 1and 2 were applied to calculations. Table 3 presents the predicted FEA and analytical burstpressures (ANA) of two flaws compared to the experimental results (EXP).

Table 3. Comparison of repaired tubes.

Defect Type Length(mm) ×Width (mm)

Flaw Depth d/t(%)

Burst Pressure,MPa

(Unrepaired)

EXP BurstPressure, MPa

(Repaired)

FEA BurstPressure, MPa

(Repaired)

ANA BurstPressure, MPa

(Repaired)Reference

Intact steel pipe(Unflawed) 0% 45.85 N/A N/A N/A

[18]Axisymmetric 50% 29.99 43.80 43.29 44.15

152.4 × 152.4 50% 30.34 43.10 N/A 44.15

Intact steel pipe(Unflawed) 0% 27.59 N/A N/A N/A

[23]133 × 102 60% 13.8 29.06 28.32 46.4

In Figures 5 and 6, finite element analysis results for each defect at the predicted failurepressures are presented. Figure 5 shows that the highest failure inducing stresses occurredin the center of the axisymmetric defect region of 50% pipe wall loss depth. The failurepressure was determined when the circumferential stress of the composite reached itsmaximum value at 576 MPa, as provided in [18]. At the burst pressure, the hoop stress at

Materials 2021, 14, 6393 10 of 18

the steel pipe reached 460 MPa. For the other case of the tube wall volumetric flaw withdimensions of 133× 102 and 60% pipe wall loss depth, as can be seen in Figure 6a, the burstfailure criterion was met in the steel outside the repair area. This criterion states that thetube wall fails when the circumferential stress of the pipe steel exceeds 530 MPa [23];however, the stress in the composite remains below the failure stress (678 MPa). Figure 6bshows the comparison between the numerical simulation result and the experimentalone [23] with respect to the rupture area. It was also noted that the analytical solutionpredicted that a repair thickness of 6 mm could increase the burst pressure to 46 MPa.Since the maximum internal pressure is 28.5 MPa, the rupture will occur outside the repairzone. In both cases, the predicted burst pressures, 43.29 MPa and 28.32 MPa, were closeto the experimentally obtained values of 43.80 MPa and 29.06 MPa. Therefore, a goodagreement between the results was obtained.

Figure 5. FEA predicted radial stress, steel and composite hoop stresses at the center of the 50% pipewall loss axisymmetric defects, Pburst = 43.29 MPa (full expansion).

Furthermore, as can be seen in Table 3, for an unrepaired defected pipe, the resultingburst pressures for axisymmetric 152.4 × 152.4 flaw were 29.99 MPa and 30.34 MPa whenthe metal loss depth was 50%. As was mentioned above, the effect of feature width ismarginal when the defect width is sufficient [27,28]. This fact can justify the use of anaxisymmetric numerical model to analyze the repair of pipelines with the application ofcomposite overwrap systems.

Graphs of the circumferential stress and its corresponding strain at the center of thedefect with dimensions of 152.4 × 152.4 in the cross section of materials were shown inFigure 7. There are two discontinuities in the stress–thickness plots as the material changesfrom steel to filler and from filler to CFRP. In both the examined cases, the failure criterionwas reached first for the composite repair system. Although the failure pressures are notthe same, the maximum stress and its corresponding strain (0.0235) were the same forboth cases.

Materials 2021, 14, 6393 11 of 18

Figure 6. (a) FEA predicted radial stress, steel and composite hoop stresses at the center of the 60%pipe wall loss axisymmetric defects, Pburst = 28.32 MPa, (b) comparison of the FEA predicted rupturezone with the experimental one performed by [23].

Figure 7. Evolution of circumferential stress and strain through the thickness for 50% wall loss axisymmetric defects.

Materials 2021, 14, 6393 12 of 18

4. Composite Repair Sleeve Sizing at Design Pressure

In order to evaluate the validity of the suggested new solution for providing theminimum laminate sleeve thickness to effectively renovate a corroded pipeline at designpressure, a series of numerical representations of repairs were sized for corrosion fea-tures ranging in depth from 0.1t0 to 0.9t0. The wrap thickness tc was calculated usingthe developed approach, as well as the ASME PCC-2 code [6] and the ISO standard [7].Consequently, using ANSYS software package, all repair systems resulting from each of theabove methodologies were simulated. The purpose of the FEA is to estimate the hoop strainon the inner side of the composite sleeve and the outer side of the feature. Artificial metallosses were incorporated outside the pipe with the longitudinal length of features equal to152.4 mm, axisymmetric widths, and uniform depths ranging from 10% to 90% of the wallthickness. Subsequently, the overwrap was applied circumferentially after filling defectswith the putty filler. In the present analysis, the sleeve used for the reinforcement wasassumed to be a fiber-glass reinforced epoxy composite. Table 4 provides the mechanicalproperties of the laminate and the filler material from work [29], respectively. It is assumedthat the repair lifetime is 10 years, similarly as was adopted in [7]. However, the allowablecircumferential laminate strain is 0.3%, as is assumed in Article 4 of ASME PCC-2.

Table 4. Laminate and filler material mechanical properties.

Polymer-Based Laminate

Modulus in the hoop direction Eθ (MPa) 23,800Modulus in the axial direction Ea (MPa) 24,500Modulus in the radial direction Er(MPa) 11,600

Poisson’s ratio vra 0.071Poisson’s ratio vaθ 0.107Poisson’s ratio vrθ 0.1

Shear modulus Gra (MPa) 2600Shear modulus Gaθ (MPa) 4700Shear modulus Grθ (MPa) 3600

Laminate allowable strain εc(mm/mm) 0.003Filler Material

Young’s Modulus Ep (MPa) 1.740Poisson’s ratio vp 0.45

5. Results and Discussion

Table 5 and Figure 8 summarize and plot the analytical calculation results for thecomposite repair configurations considered in this paper. These values were obtained usingthe developed approach, ASME PCC-2, as well as ISO/TS 24817. All the reinforcementscorrespond to design conditions, including the design pressure of the tube (calculated as14.68 MPa from Equation (49)), and the metal loss depths varying from 10 to 90% of thethickness of the intact pipe. From Figure 8, it can be seen that all three methods result inlaminate thickness increasing with the metal loss radial size. For volumetric flaws witha depth d/t = 10% to 90%, the ISO/TS-24817 standard resulted in excessive overwrapthickness compared to ASME PCC-2 and the proposed approach. The presented algorithmled to even smaller laminate thickness compared to the results of PCC-2 standard providingrelatively small sleeve thickness. It should be highlighted that, in contrast to ISO/TS 24817standard, both PCC-2 methodology and the proposed solution did not require applicationof composite repairs for the defect depths ranging from 25% to 45% of the intact tube.Taken into consideration the Pf /MAOP ratio values, it is noted that the presented approachprovides the sleeve thickness only when Pf /MAOP ≤ 1.25. Therefore, it can be observedthat the proposed solution provides the overwrap thickness for the metal losses with a50% depth of the tube wall thickness, whereas, according to B31.G code, such corrosionanomalies are acceptable, however, without reinforcement. Thus, the results of sizingwith a methodology developed in the current paper are fully consistent with that of theB31.G standard, recommending the reinforcement if the condition for the steel pipe wall

Materials 2021, 14, 6393 13 of 18

loss, Pf /MAOP < 1.25, is not met. ISO/TS 24817 and ASME PCC-2 codes for sizing thecomposite sleeves lead to unnecessary repairs of steel tube wall volumetric flaws rangingfrom 10% to 50% and from 30% to 50%, respectively, for the two standards. Furthermore,the effect of external pressure Pext, such as water hydrostatic pressure, on the thicknessof the overwrap is shown in Figure 8. As can be observed, the thickness of the laminatedecreases with the increasing external pressure around the tube. At Pext = 2.5 MPa, a repaircondition starts from a feature depth of 60% instead of 50%, as in the case of zero externalpressure. In this case, the composite sleeve thickness is 0.44 mm instead of 3.47 mm.When increasing the external pressure to 5.0 MPa, it is possible to apply a polymer-basedoverwrap for defects with a depth starting from 70% instead of 50%, as in the case of zeroexternal pressure, and a thickness of 0.67 mm instead of 6.89 mm. Therefore, for mediumcorrosion anomalies ranging from 50% to 65%, the proposed approach provides the sleevethickness of 96% to 42% smaller than in the case of ASME PCC-2, and 32% to 4% smallerfor deep metal losses (70% to 90%). With regard to ISO/TS 24817 for the external pressureof 5.0 MPa, the proposed method reduced the fiber-glass thickness from 97.5% to 54%for medium defects depths ranging from 50% to 65%. For the depth of pipe wall metallosses greater than 70%, the reduction of the sleeve thickness is by 43% to 8.4% comparedto ISO/TS 24817 for the external pressure of 5.0 MPa. Unlike PCC-2 and ISO standards,the proposed solution does not provide any composite reinforcement for small depths ofvolumetric flaws ranging from 10% to 45%.

Figure 8. Composite thickness calculated analytically at the design pressure.

The results presented in Figure 9 are hoop strain obtained from the finite elementanalysis at the design load of 14.68 MPa for depths of features ranging from 10% to 90%.Figure 9a shows the hoop strain εs

θ,1 in the steel beneath the putty material, and Figure 9bshows the hoop strain εc

θ,2 in the inner surface of the laminate. The most significant observa-tion concerns the tube wall losses with a depth of 50%, whereas the developed methodologyrecommends repair when the defected steel pipe wall begins to plasticize. This confirms theabove observation concerning the depth starting from which reinforcement of the flawedsteel tube is necessary.

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Figure 9. FEA predicted hoop strain at the design pressure: (a) outer surface of the pipe (middle ofcorrosion feature), (b) inner surface of the composite repair system.

By comparing the obtained pipe hoop strains, it was clearly observed that the hoopstrain, given by the developed method, in the corroded region was greater than thoseobtained by PCC-2 and ISO. The deformation given by the presented approach increasedconsiderably with an increase in the metal loss depth and slightly exceeded the elastic limitof the steel. It should be noted that the developed calculation procedure tolerates a certainrate of strain-hardening for the steel material. For all the simulations, the stress is assumedto be 320 MPa. On the other hand, both PCC-2 and ISO standards increased with the defect

Materials 2021, 14, 6393 15 of 18

depth in a similar way with a small deviation. This deviation depends on the allowablestress taken in the design, which is equal to the value of SMYS for PCC-2 and 0.72 SMYSfor ISO. It can also be noted that, for these methods, the steel behavior is assumed to beelastic perfectly plastic; however, the steel has exceeded its allowable stress.

Table 5. Sizing of composite sleeve thickness as a function of relative metal loss depth.

Pd [MPa](Equation

(49))

dt [%] Pf

MAOP

tc [mm]

ASME PCC-2(S = SMYS)

ISO/TS24817(S = 0.72SMYS)

Developed(Pext = 0 MPa)

Developed(Pext = 2.5 MPa)

DevelopedPext = 5 MPa

14.68(Pressure Pi

to berecovered)

10 1.86 0 1.73 0 0 0

15 1.79 0 2.60 0 0 0

20 1.73 0 3.46 0 0 0

25 1.66 0 4.33 0 0 0

30 1.59 0.48 5.19 0 0 0

35 1.52 1.68 6.06 0 0 0

40 1.45 2.88 6.92 0 0 0

45 1.37 4.08 7.79 0 0 0

50 1.30 5.29 8.65 0.22 0 0

55 1.22 6.49 9.52 1.83 0 0

60 1.14 7.69 10.38 3.47 0.44 0

65 1.05 8.89 11.25 5.16 2.01 0

70 0.97 10.09 12.11 6.89 3.61 0.67

75 0.88 11.29 12.98 8.66 5.25 2.2

80 0.79 12.49 13.84 10.47 6.93 3.76

85 0.69 13.70 14.71 12.34 8.65 5.36

90 0.59 14.90 15.57 14.26 10.42 7.00

As shown in Figure 9b, when the volumetric flaw depth increased beyond 50%,plasticity was induced in the corroded zone of the steel pipe, and the mechanical load(internal pressure in the considered case) carried by the corroded area was transferred tothe laminate through the filler material. As the feature depth increased, the strain of sleeveincreased while remaining less than the allowable strain, εc = 0.3% , for polymer-basedmaterial. Although all methods presented approximately the same strain regarding thedeepest defects, the hoop strain obtained with the developed algorithm was important fora medium depth of wall material losses. This was due to the efficiency of the proposedmethod to give smaller repair thickness while providing a laminate material strain lowerthan the admissible one.

6. Conclusions

In this paper, an analytical formulation and FEA studies were conducted in order topresent a new cost-effective method for determining the composite sleeve thickness forthe corroded pipe repairs. The analytical procedure proposed in the form of an algorithmis validated using experimental data taken from the literature. The validation of themethodology showed that this method can predict economical and efficient compositerepair thicknesses at limit load conditions. The proposed algorithm is compared to ASME,PCC-2 and ISO/TS 2481 standards using the results of a series of finite element analyses.By analyzing the obtained results, the following conclusions can be drawn:

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1. The composite overwrap sizing calculated according to ASME PCC-2 and ISO/TS2481 standards is conservative with respect to the obtained sleeve thickness andresults in unnecessary repairs of the steel pipe wall thinning, particularly for smalldepths of material losses. For a medium depth of metal losses, ranging from 50% to65% of the tube wall, in the case of the new developed solution, the sleeve thicknesswas reduced as follows:

- by 96% to 42% compared to the results of ASME PCC-2,- by 97.5% to 54% compared to the results of ISO/TS 2481.

2. For the deepest pipe wall metal losses, starting from 70% of wall thickness, the appliedsizing algorithm reduces the wrap thickness as follows:

- by 32% to 4% compared to the results of ASME PCC-2,- by 43% to 8.4% compared to the results of ISO/TS 2481.

3. The presented methodology takes into consideration an effect of the external pressuresurrounding the tube, as in the case of offshore pipelines, in which the thickness ofthe fiber-glass sleeve is even less.

4. The proposed approach predicts the burst pressure of the defected pipes repaired witha composite overwrap system for practical applications. Due to this fact, the authorsare going to conduct experiments to validate the burst pressure of steel tubes repairedwith the use of the developed sleeve sizing procedure.

Author Contributions: D.D.: conceptualization, methodology, software, validation, formal analysis,writing—original draft, writing—review and editing, visualization; G.T.: methodology, software,validation, formal analysis, resources, supervision; M.W.: writing—review and editing, visualization,supervision, project management; M.A.: software, validation, writing—original draft. All authorshave read and agreed to the published version of the manuscript.

Funding: This research was funded by the Warsaw University of Technology within the IDUB-OpenScience Program.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: All data generated or analyzed during this study are included in thispublished article.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Dext Outside diameter of the steel tubePrecovered Pressure to be recoveredPd Internal design pressure of the pipelinePlive Live pressurePi Actual internal pressurePext External pressurePc,j Contact pressure at the location j

Pf Burst pressure of the steel pipetc Minimum required thickness of the composite sleevets Remaining thickness of the pipe wall in the corroded zonet0 Thickness of the steel pipeεc Composite allowable strainS Specified minimum yield stress of steeln Strain hardening exponentK Material strength coefficient

R0, R1, R2 and R3Internal radius of the steel tube, internal radius of corrosion defect, external radiusof steel tube, and internal radius of composite repair

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α0, α1, α2 and α3 Dimensionless geometric ratioσy Actual yield stress

σjθ,i, σ

ja,i and σ

jr,i

Stress components, respectively, in hoop, axial, and radial directions. Theindices i and j denote, respectively, the contact pressure location and thematerial type

εjθ,i, ε

ja,i and ε

jr,i

Strain components, respectively, in hoop, axial, and radial directions. Theindicesi and j denote, respectively, the contact pressure location and thematerial type

Ecθ , Ec

a and Ecr

Elastic moduli of the composite, respectively, in the circumferential, axial,and radial directions

vcra, vc

aθ and vcrθ Composite material Poisson’s ratio

Gcra, Gc

aθ and Gcrθ

Shear moduli of the composite, respectively, in the circumferential, axial,and radial directions.

vp Putty Poisson’s ratioc Corrosion defect half lengthw Corrosion defect widthd Corrosion defect depthz Normalized defect lengthM Folias factorFET Safety factorsMAWP The maximum allowable working pressureMOP The maximum operating pressure

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